(a) Imaging scene with a partially-reflecting object (shown in gray dashed line). 1 Examples of active imaging scenarios in which the scene response is a sum of responses from multiple reflectors. This is known as the problem of multi-depth reconstruction from full-waveform measurements. For such scenes, one can analyze multiple light returns to fully reconstruct the multiple depths present in the field-of-view. 1, scenes that include partially-reflective or partially-occluding objects have complex patterns of light being reflected at different depths even at a single pixel. Time-of-flight methods for 3D acquisition illuminate the scene and analyze the backreflected light signal. The ability to acquire 3D structure of a scene is important in many applications, such as biometrics, terrestrial mapping, and gaming. In terms of root mean-square error, this is a factor of 4.2 improvement over the conventional method of Gaussian-mixture fitting for multi-depth recovery. We experimentally demonstrate that the proposed framework is able to accurately reconstruct the depth features of an object that is behind a partially-reflecting scatterer and 4 m away from the imager with root mean-square error of 11 cm, using only 19 signal photon detections per pixel in the presence of moderate background light. We interpret the multi-depth reconstruction problem as a sparse deconvolution problem using single-photon observations, create a convex problem through discretization and relaxation, and use a modified iterative shrinkage-thresholding algorithm to efficiently solve for the optimal multi-depth solution. Our active imaging method models the single-photon detection statistics from multiple reflectors within a pixel, and it also exploits the fact that a multi-depth profile at each pixel can be expressed as a sparse signal. We present an imaging framework that is able to accurately reconstruct multiple depths at individual pixels from single-photon observations. Note: Author names will be searched in the keywords field, also, but that may find papers where the person is mentioned, rather than papers they authored.Use a comma to separate multiple people: J Smith, RL Jones, Macarthur.
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